Question: $\dfrac{d}{dx}\left(x^{-4}\right)=$
Explanation: The derivative can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is a negative number.) $\begin{aligned} &\phantom{=}\dfrac{d}{dx}\left(x^{-4}\right) \\\\ &=-4x^{-4-1} \gray{\text{The power rule}} \\\\ &=-4x^{-5} \end{aligned}$ In conclusion, we found that $\dfrac{d}{dx}\left(x^{-4}\right)=-4x^{-5}$. This can also be written as $-\dfrac{4}{x^5}$ (all equivalent forms are accepted).